Bifurcation Analysis and Circuit Implementstion of a Simple Chaos Generator.pdf

Bifurcation Analysis and Circuit Implementation of a Simple Chaos Generator Guo Qun ZHONG, Kit Sang TANG, Guanrong CHEN and Kim F. MAN Dep artment of Electronic Engineering, City University of Hong Kong, Hong Kong, P.R. China gchen@e e.cityu.edu.hk Abstr act| A nonlinear controller is pro- In this pap er, a nonlinear state feedback anti- p osed for chaos generation in an arbitrarily controller is formulated for generating chaos from an given lower-order linear autonomous system. otherwise non-chaotic lower-order linear autonomous The only nonlinearity in the controller is system. The main idea comes from our earlier research a piecewise quadratic function of the form along the line of chaos generation via state feedback g ( ) =  j j. A general two-dimensional linear control (Chen and Lai, 1998; Kunin and Chen, 2000; autonomous system is used for illustration. Tang et al., 2001; Wang and Chen, 2000a; Wang and Bifurcation analysis and chaos verication are Chen, 2000b). given by numerical continuation techniques and the Shilnikov theorem. Both computer simu- To verify the existence of the intro duced chaotic lation and circuit implementation demonstrate attractor, we fo cus on an one-parameter analysis for the chaotic dynamics generated by this simple the p erio dic orbits and the homo clinic bifurcation anti-controller. analysis. The bifurcation analysis of the anti- controlled system is based on the continuation K ey w or ds| Bifurcation, chaos generator, techniques using